I show you how to multiply
three coordinates with three 2-d bases to move
left and right with cosine and up and down with sine
to the right spot, like on a piece of paper.

A 2-D ijk-Picture of a 3-D graph can be found
in the calc3book.pdf from mecmath.net.
That had let me think how to do that on the screen.

The following algorithm covers most of
the steps i figured out already to do the standard
transforms before projecting with this nice formula.

All three angles start at 0
α := x-Axis Angle
β := y-Axis Angle
γ := z-Axis Angle
u{x,y,z} := Unit of the vectors
of the projection base.
should all have same size, .
else the thing stretch to a side
when rotating

The projection is a 2x3 matrix.
I had the idea to use three two dimensional vectors.
The idea came from orthogonal bases and
the memory of the ijk-Notation Picture
showing the three base vectors on the axes.

Each column holds a base vector for x,y or z.
[len*cos({x,y,z}angle), len*sin({x,y,z}angle)]
Instead of taking numbers i took the unit circle
and angles.

P =

ux*Math.cos(α)

uy*Math.cos(β)

uz*Math.cos(γ)

ux*Math.sin(α)

uy*Math.sin(β)

uz*Math.sin(γ)

In the following steps i first get the points.
Then i apply the local transformations.